SOLUTION: Help please
A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 6 ft shorter than the length of the ladder. How high up the sid
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A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 6 ft shorter than the length of the ladder. How high up the sid
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Question 1040943: Help please
A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 6 ft shorter than the length of the ladder. How high up the side of the building is the top of the ladder if that distance is 3 ft less than the length of the ladder?
The top of the ladder is _____ ft up the side of the building. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A ladder is leaning against a building.
The distance from the bottom of the ladder to the building is 6 ft shorter than the length of the ladder.
How high up the side of the building is the top of the ladder if that distance is 3 ft less than the length of the ladder?
:
Let L = the length of the ladder
This is a Pythagorean problem where
L = the hypotenuse, the length of the ladder
(L-6) = one leg the distance from the base of the ladder to the building
(L-3) = the other leg, the height from the ground to the top of the ladder
:
(L-6)^2 + (L-3)^2 = L^2
FOIL
(L^2 - 12L + ) + (L^2 - 6L + 9) = L^2
combine like terms
L^2 + L^2 - L^2 - 12L - 6L + 36 + 9 = 0
L^2 - 18L + 45 = 0
Factors to
(L-3)(L-15) = 0
L = 3
and
L = 15 ft is the reasonable answer for the length of the ladder
:
The top of the ladder is _____ ft up the side of the building.
15 - 3 = 12 ft up the side of the building
:
:
Check this, the two sides would be 9 and 12
L =
L = !5
